Chapter_5_MultiPathPropagation Neces.pdf

Multiple path propagation

1. Wireless and Mobile Communication
Multi-Path Wave Propagation and Fading
Faculty of Electrical and Computer Engineering
Bahir Dar University
BIT
2009
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 1 / 40

2. Outline
1
Multipath Propagation
2
Doppler shift
3
Impulse Response Model of a Multipath Channel
4
Power Delay Prole
5
Parameters of Mobile Multipath Channels
6
Classication of Multipath Channels
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3. Multipath Propagation
Multipath Propagation
In wireless telecommunications, multipath is the propagation
phenomenon that results in radio signals reaching the receiving
antenna by two or more paths
Causes of multipath include atmospheric ducting, ionospheric
reection and refraction, and reection from water bodies and
terrestrial objects such as mountains and buildings
The eects of multipath include constructive and destructive
interference, and phase shifting of the signal
In digital radio communications (such as GSM) multipath can cause
errors and aect the quality of communications.
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 3 / 40

4. Multipath Propagation
Multipath & Small-Scale Fading
Small-scale fading
and phase that can be experienced as a result of small changes (as
small as a half wavelength) in the spatial positioning between a
receiver and a transmitter.
Small-scale fading manifests itself in two mechanisms:
of the signal
channel
Fading
the radio over a short period of time or travel distance so that the
large scale path loss eect may be ignored
Fadingis caused by interference between two or more versions of the
transmitted signal which arrive at the receiver at slightly dierent
times
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 4 / 40

5. Multipath Propagation
Multipath Fading Eects
Multipath in the radio channel creates small-scale fading eects
The three most important eects are:
1
Rapid changes in signal strength over a small travel distance or time
interval
2
Random frequency modulation due to varying Doppler shifts on
dierent multipath signals
3
Time dispersion or echoes caused by multipath propagation delays
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 5 / 40

6. Multipath Propagation
Factors Inuencing Fading
The following physical factors inuence small-scale fading in the radio
propagation channel:
1
Multipath propagation
dierent paths, constructive and destructive interference occurred as
well as phase shifting of the signals
2
Speed of the mobile
and the mobile results in random frequency modulation due to dierent
doppler shifts on each of the multipath components.
3
Speed of surrounding objects
multipath components If the surrounding objects move at a greater
rate than the mobile , then this eect dominates the small scale fading
4
Transmission Bandwidth of the signal
bandwidth is greater than the "bandwidth" of the multipath channel
(quantied by coherence bandwidth), the received signal will be
distorted
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 6 / 40

7. Doppler shift
Doppler shift
The shift in received signal frequency due to motion)is directly
proportional to the velocity and direction of motion of the mobile
with respect to the direction of arrival of the received multipath wave
Lis the dierence in path length traveled by the wave
from source s to the mobile at points X and Y
L=dcos=vtcos
tis the time required for the mobile to travel from
point X to Y
The phase change in the received signal due to the
dierence in path length is = 2L=
The apparent change in frequency
fd= =2t=vcos=(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 7 / 40

8. Doppler shift
Doppler shift
The Doppler shift is positive (i.e., the apparent received frequency is
increased), if the mobile is moving toward the direction of arrival of
the wave.
The Doppler shift is negative (i.e. the apparent received frequency is
decreased), if the mobile is moving away from the direction of arrival
of the wave.
Multipath components from a CW signal which arrive from dierent
directions contribute to Doppler spreading of the received signal, thus
increasing the signal bandwidth
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 8 / 40

9. Impulse Response Model of a Multipath Channel
Impulse Response Model of a Multipath Channel
The small scale fading can be directly related to the impulse response
of the mobile radio channel
The impulse response is a wideband channel characteristics
It contains all information necessary to analyze any type of radio
transmission through the channel
Mobile radio channel may be modeled as a linear lter with a
time varying impulse response, where time variation is due to
receiver motion in space
For a, the channel between the transmitter and the
receiver can be modeled as a
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 9 / 40

10. Impulse Response Model of a Multipath Channel
Impulse Response
The dierent multipath waves have propagation delays which vary
over dierent spatial locations of the receiver
The impulse response should be a function of the receiver position
Therefore the channel impulse response can be expressed ash(d;t)
Let,x(t) andy(d;t) are transmitted and received signals respectively,
then
y(d;t) =x(t)h(d;t) =
Z
1
1
x()h(d;t)d (1)
For a causal systemh(d;t) = 0 fort<0
y(d;t) =
Z
t
1
x()h(d;t)d d=vt
y(t;t) =
Z
t
1
x()h(t;t)d
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11. Impulse Response Model of a Multipath Channel
Impulse Response
Since v is constanty(t;t) is just a function of t and then,
y(t) =
Z
t
1
x()h(t;t)d=x(t)h(t;t) =x(t)h(d;t)
It is clear that the mobile radio channel can be modeled as a linear
time varying channel where the channel changing with time and
distance
vcan be assumed constant over a short time or distance interval
x(t) represent the transmitted bandpass waveform
y(t) the received signal waveform
h(t; ) the impulse response of the time varying multipath radio
channel
trepresents the time variations due to motion
represents the channel multipath delay for a xed value oft
y(t) =
Z
t
1
x()h(t; )d=x(t)h(t; )
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12. Impulse Response Model of a Multipath Channel
Discretizing the multipath delay axis
Discretize the multipath axis delay of the impulse response into equal
time delay segments called excess delay bins
Each bin has a time delay width =i+1i
0= 0 (the rst arriving signal at the receiver)
1= , theni=i i= 0 toN1
N is the total number of possible equally-spaced multipath
components
Quantizing the delay bins determines the time delay resolution of the
channel model
The useful frequency span of the model = 2=
The model can be used to analyze transmitted RF signals having
bandwidths which are less than 2=
The maximum excess delay =N
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 12 / 40

13. Impulse Response Model of a Multipath Channel
Discretizing the multipath delay axis
The received signal consists of a series of
attenuated,
time delayed,
phase shifted replicas of the transmitted signal
The baseband impulse response of a multipath channel can be
expressed as
hb(t; ) =
N1
X
i=0
ai(t)exp[j2fci(t) +i(t; )](; i(t)) (2)
ai(t; ))the amplitude of thei
th
multipath component
i)the excess delay of thei
th
multipath component
2fci(t))the phase shift due to free space propagation of thei
th
multipath component
i(t; ))any additional phase shifts which are encountered in the
channel
(:) is the the unit impulse function which determines the specic
multipath bins that have components at time t and excess delaysi
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14. Impulse Response Model of a Multipath Channel
Discretizing the multipath delay axis
In general, the phase term can be simply represented by a single
variable(t; i)
and(i(t)) is the unit impulse function which determines the
specic multipath bins that have components at timetand excess
delaysi
If the channel impulse response is assumed to be time invariant, then
the channel impulse response may be simplied as
hb(t; ) =
N1
X
i=0
aiexp(ji)(i) (3)
When measuring or predictinghb(t) a probing pulsep(t) which
approximates a delta function is used at the transmitter
That is,
p(t)(t)
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 14 / 40

15. Impulse Response Model of a Multipath Channel
Discretizing the multipath delay axis
An example of the time varying discrete-time impulse response model
for a multipath radio channel
Discrete models are useful in simulation where modulation data must
be convolved with the channel impulse response
Discretize the multipath delay axis
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 15 / 40

16. Power Delay Prole
Power Delay Prole
For small scale fading, the power delay prole of channel can be
found using the spatial average ofjhb(t;)j
2
over the local area.
It P(t) has time duration much smaller than the impulse response of
multipath channel, the received power delay prole in local area can
be
P(t;)kjhb(t;)j
2
(4)
Where the gain k relates the power of input pulse to the received
power
Power delay proles are generally represented as plots of relative
received power as a function of excess delay with respect to a xed
time delay reference
Power delay proles are found by averaging instantaneous power delay
prole measurements over a local area in order to determine an
average small-scale power delay prole
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17. Power Delay Prole
Measuring PDPs
Power Delay Proles
Are measured by channel sounding techniques
Plots of relative received power as a function of excess delay
They are found by averaging intantenous power delay measurements
over a local area
Local area: no greater than 6m outdoor
Local area: no greater than 2m indoor
Samples taken at l/4 meters approximately
For 450 MHz 6 GHz frequency range.
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18. Power Delay Prole
Typical power delay prole plots
Outdoor channels, determined from a large number of closely sampled
instantaneous proles
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19. Power Delay Prole
Typical power delay prole plots
indoor channels, determined from a large number of closely sampled
instantaneous proles
Inside store at 4 GHz
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20. Parameters of Mobile Multipath Channels
Time Dispersion Parameters
In order to compare dierent multipath channels and to develop some
general design guidelines for wireless systems, parameters which
grossly quantify the multipath channel are used
The mean excess delay,
(XdB)
the power delay prole
The time dispersive properties of the wide band multipath channels
are most commonly quantied by their mean excess delay () and rms
delay spread ()
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 20 / 40

21. Parameters of Mobile Multipath Channels
Time Dispersion Parameters
The mean excess delay is the rst moment of the power delay prole and is dened
as
=
P
k
a
2
kk
P
k
a
2
k
=
P
k
P(k)(k)
P
k
P(k)
The rms delay spread is the square root of the second central moment of the
power delay prole
=
q


2
()
2
where


2
=
P
k
a
2
k
2
k
P
k
a
2
k
=
P
k
P(k)(
2
k)
P
k
P(k)
Maximum Excess Delay (X dB):
Dened as the time delay value after which the multipath energy falls to X
dB below the maximum multipath energy (not necessarily belonging to the
rst arriving component).
It is also called excess delay spread
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22. Parameters of Mobile Multipath Channels
Time Dispersion Parameters
RMS Delay Spread
The values of time dispersion parameters also depend on the noise threshold (the
level of power below which the signal is considered as noise).
If noise threshold is set too low, then the noise will be processed as multipath and
thus causing the parameters to be higher
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 22 / 40

23. Parameters of Mobile Multipath Channels
Delay Spread, Coherence BW
Describes the time dispersive nature of a channel in a local area
A received signal suers spreading in time compared to the
transmitted signal
Delay spread can range from a few hundred nanoseconds for indoor
scenario up to some microseconds in urban areas
The coherence bandwidthBctranslates time dispersion into the
language of the frequency domain.
It species the frequency range over which a channel aects the
signal spectrum nearly in the same way, causing an approximately
constant attenuation and linear change in phase
The rms delay spread and coherence bandwidth are inversely
proportional to each other
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 23 / 40

24. Parameters of Mobile Multipath Channels
Coherence Bandwidth (Bc)
Range of frequencies over which the channel can be considered at
(i.e. channel passes all spectral components with equal gain and
linear phase)
It is a denition that depends on RMS Delay Spread
Two sinusoids with frequency separation greater thanBcare aected
quite dierently by the channel
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25. Parameters of Mobile Multipath Channels
Coherence Bandwidth
Frequency correlation between two sinusoids: 0Cr1;r21
If we dene Coherence Bandwidth (Bc) as the range of frequencies
over which the frequency correlation is above 0.9, then
Bc=
1
50
)is rms delay spread
If we dene Coherence Bandwidth as the range of frequencies over
which the frequency correlation is above 0.5, then
Bc=
1
5
This is called 50% coherence bandwidth
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26. Parameters of Mobile Multipath Channels
broadcast radio communication system
Example:
For a multipath channel,is given as 1.37ms
The 50% coherence bandwidth is given as: 1=5= 146kHz
This means that, for a good transmission from a transmitter to a
receiver, the range of transmission frequency (channel bandwidth)
should not exceed 146kHz, so that all frequencies in this band
experience the same channel characteristics.
Equalizers are needed in order to use transmission frequencies that are
separated larger than this value
This coherence bandwidth is enough for an AMPS channel (30kHz
band needed for a channel), but is not enough for a GSM channel
(200kHz needed per channel)
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 26 / 40

27. Parameters of Mobile Multipath Channels
Doppler Spread and Coherence time
Delay spread
nature of the channel in a local area.
They dont oer information about the time varying nature of the
channel caused by relative motion of transmitter and receiver
Doppler Spread
the time varying nature of the channel in a small-scale region
Time varying nature of channel caused either by relative motion
between BS and mobile or by motions of objects in channel are
categorized byBDandTc
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 27 / 40

28. Parameters of Mobile Multipath Channels
Doppler Spread
Measure of spectral broadening caused by motion
We know how to compute Doppler shift:fd
Doppler spread,BD, is dened as the maximum Doppler shift:
fm=v=
IfTxsignal bandwidth (Bs) is large such thatBs>>BDthen eects
of Doppler spread are NOT important so Doppler spread is only
important for low bps (data rate) applications (e.g. paging), slow
fading channel
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29. Parameters of Mobile Multipath Channels
Coherence Time
Coherence time is the time duration over which the channel impulse
response is essentially invariant
If the symbol period of the baseband signal (reciprocal of the
baseband signal bandwidth) is greater the coherence time, than the
signal will distort, since channel will change during the transmission of
the signal
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30. Parameters of Mobile Multipath Channels
Coherence Time
Coherence time is also dened as:
Tc
9
16f
2
m
=
0:423
fm
(5)
Coherence time denition implies that two signals arriving with a time
separation greater than TC are aected dierently by the channel
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31. Classication of Multipath Channels
Classication of Multipath Channels
Depending on the relation between signal parameters (bandwidth and
symbol period) and channel parameters (delay spread and Doppler
spread) dierent signals undergo dierent types of fading
Based on delay spread the types of small scale fading are
1
Flat fading
2
Frequency selective fading
Based on Doppler spread the types of small scale fading are
1
Fast fading
2
Slow fading
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32. Classication of Multipath Channels
Flat fading
Occurs when the
Occurs when
than the Delay Spread of the channel
The BW of the signal is narrow compared to the channel at fading
BW
The channel has a at transfer function with almost linear phase,
thus aecting all spectral components of the signal in the same way
Typical at fading channels cause deep fade
Thus may require 20 to 30 dB transmitter power increase to achieve
low bit error rates during times of deep fade as compared to systems
operating over non-fading channels
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33. Classication of Multipath Channels
Flat fading
Occurs when
Bs<<Bcand Ts>>
whereTsis the reciprocal bandwidth (eg. symbol period) andBsis the
bandwidth, respectively, of the transmitted modulation andandBc
are the rms delay spread and coherence bandwidth, respectively, of the
channel
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 33 / 40

34. Classication of Multipath Channels
Frequency Selective Fading
The channel possesses a constant gain and linear phase response over
a bandwidth that is smaller than the bandwidth of the transmitted
signal
The channel impulse response has a multipath delay spread which is
greater than the reciprocal bandwidth of the transmitted message
waveform.
It is due to time dispersion of the transmitted symbols within the
channel.
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 34 / 40

35. Classication of Multipath Channels
Frequency Selective Fading
Occurs when
Bs>Bcand Ts<
The received signal includes multiple versions of the transmitted
waveform which are attenuated (faded) and delayed in time, and
hence the received signal is distorted.
The channel induces inter-symbol interference (ISI).
Certain frequency components in the received signal spectrum have
greater gains than others.
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 35 / 40

36. Classication of Multipath Channels
Fading Eects Due to Doppler Spread
How rapidly the transmitted baseband signal changes as compared to
the rate of change of the channel?
The channel impulse response changes rapidly within the symbol
durationTs>Tc(Bs<BD))Frequency Dispersion (signal
distortion)
)Fast Fading Rate of change due to motion
In the case of at fading channel we can approximate the impulse
response to be simply a delta function
(Bahir Dar Institute of Technology)Wireless and Mobile Communication 2009 36 / 40

37. Classication of Multipath Channels
Fast fading
Flat fading, fast fading channel
Is a channel in which the amplitude of the delta function varies faster than
the rate of change of the transmitted baseband signal
Frequency selective, fast fading channel
The amplitudes, phases, and time delays, of any one of the multipath
components vary faster that the rate of change of the transmitted signal In practice fast fading is only occurs for very low data rate
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38. Classication of Multipath Channels
Slow Fading
In slow fading channel, the channel impulse response changes at a
rate much slower than the transmitted baseband signal s(t)
The channel may be assumed to be static over one or several
reciprocal bandwidth intervals
Ts<<Tc
Bs>>BD
It should be emphasized that fast and slow fading deal with the
relationship between the time rate of change in the channel and the
transmitted signal, and not with the propagation path loss models
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39. Classication of Multipath Channels
Summery of Fading Types
Figure:
(a) Symbol period; and (b) baseband signal bandwidth
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40. Classication of Multipath Channels
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